An uncontested divorce is one where both people agree to end the marriage and agree on the terms. Nobody goes in front of a judge to argue. It is mostly a paperwork process.
What makes it uncontested
Agreement on the terms, not just on the divorce. Property, any support, and anything to do with children all have to be settled between you before the papers are filed.
If you agree on ending the marriage but not on the terms, that is a contested divorce and it runs differently.
The order things happen in
A summons is filed with the county clerk and the case gets an index number. The other spouse is served, or signs an affidavit accepting service, which is the usual route when both people are cooperating.
A settlement agreement is drawn up and signed covering the terms. The full packet of judgment papers is then submitted to the court.
A judge reviews the papers and signs the judgment of divorce. It is entered with the clerk, and that entry is the point at which the marriage legally ends.
How long it takes
That depends on the county and on how quickly the paperwork comes back signed. Court backlogs vary and they are outside anyone's control, so a firm date is not something an honest answer includes.
The part that is within your control is how fast the agreement gets settled and the documents get signed. That is usually what decides whether a case takes months or much longer.
This page is general information about how the process works in New York. It is not legal advice and it does not create an attorney-client relationship. Whether any of it applies to you depends on your situation, which is what a consultation is for.